In the production of gears, especially bevel and hypoid gears, two types of processes are commonly employed, generating processes and non-generating processes.
Generating processes can be divided into two categories, face milling (intermittent indexing) and face hobbing (continuous indexing). In generating face milling processes, a rotating tool is fed into the workpiece to a predetermined depth. Once this depth is reached, the tool and workpiece are then rolled together in a predetermined relative rolling motion, known as the generating roll, as though the workpiece were rotating in mesh with the theoretical generating gear, the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. The profile shape of the tooth is formed by relative motion of the tool and workpiece during the generating roll.
In generating face hobbing processes, the tool and work gear rotate in a timed relationship and the tool is fed to depth thereby forming all tooth slots in a single plunge of the tool. After full depth is reached, the generating roll is commenced.
Non-generating processes, either intermittent indexing or continuous indexing, are those in which the profile shape of a tooth on a workpiece is produced directly from the profile shape on the tool. The tool is fed into the workpiece and the profile shape on the tool is imparted to the workpiece. While no generating roll is employed, the concept of a theoretical generating gear on the form of a "crown gear" is applicable in non-generating processes. The crown gear is that theoretical gear whose tooth surfaces are complementary with the tooth surfaces of the workpiece in non-generating processes. Therefore, the cutting blades on the tool represent the teeth of the crown gear when forming the tooth surfaces on the non-generated workpiece.
The relationship between the workpiece and generating gear can be defined by a group of parameters known as basic machine settings. These basic settings communicate a sense of size and proportion regarding the generating gear and the work piece and provide a common starting point for gear design thus unifying design procedures among many models of machines. The basic settings totally describe the relative positioning between the tool and workpiece at any instant.
Basic machine settings for forming gears are known in the art and one such disclosure of them can be found in Goldrich, "CNC Generation of Spiral Bevel and Hypoid Gears: Theory and Practice" The Gleason Works, Rochester, N.Y., 1990. In this publication, basic machine settings are identified as follows: (1) the radial, S, which is the distance between the cradle axis and the tool axis; (2) the tilt angle, Pi, which defines the angle between the cradle axis and tool axis; (3) the swivel angle, Pj, which defines the orientation of the tool axis relative to a fixed reference on the cradle; (4) the cradle angle, q, which defines the angular position of the tool about the cradle axis; (5) the root angle, .SIGMA., which sets forth the orientation of the work support relative to the cradle axis; (6) the sliding base, Xb, which is the distance from the machine center to the apparent intersection of the work and cradle axis; (7) the head setting, Xp, which is a distance along the work axis from the apparent intersection of the work and cradle axis to a point located a fixed distance from the workpiece; (8) work offset, Em, which defines the distance between the work axis the cradle axis; (9) rotational position of the workpiece, Wg; and, (10) rotational position of the tool, Wt, which is used in the case of face hobbing. In addition, in generating processes, it is necessary to know the ratio-of-roll, Ra, which is the ratio of the rotation of the work piece to the rotation of the cradle.
In conventional gear forming machines, the cradle angle, work rotation, and tool rotation change during generation while the other settings generally remain fixed. Two notable exceptions to this are helical motion which involves motion of the sliding base, Xb, and vertical motion which is motion in the work offset direction, Em.
Conventional mechanical machines for producing bevel and hypoid gears comprise a work support mechanism and a cradle mechanism which, during generating processes, carries a circular tool along a circular path about an axis known as the cradle axis. The cradle represents the body of the theoretical generating gear and the cradle axis corresponds to the axis of the theoretical generating gear. The tool represents one or more teeth on the generating gear.
The conventional mechanical machine meets the concept of the theoretical basic machine since nearly all machine settings correspond to theoretical basic settings. Such a machine is shown and described in the previously mentioned Goldrich publication. In the mechanical machine, the basic setting for the radial, S, is controlled by an angular machine setting known as the eccentric angle which is commonly denoted by ".beta.".
In the recent past, gear producing machines have been developed which reduce the number of machine settings necessary to orient a tool relative to a work piece. These machines transform the settings and movements of the conventional mechanical machine to a system of linear, rotational, and pivoting axes which results in a more universal yet simplified machine.
One example of a multi-axis machine is shown in U.S. Pat. No. 5,257,882 to Stadtfeld et al. In this machine, the eccentric angle, swivel angle, tilt angle, and hypoid offset settings have been eliminated but a cradle, carrying an eccentric slide, is still present on the machine.
Another multi-axis or free-form machine is shown in U.S. Pat. No. 4,981,402 to Krenzer et al. This machine comprises six axes of movement, three linear and three rotational, to orient a tool and workpiece with respect to one another. The cradle, eccentric, hypoid offset, and the angular settings to orient the tool have been eliminated. The six axes are controlled by a computer in response to setup and operating parameters of the conventional mechanical gear generating machine. The machine settings from the mechanical machine are transformed into the kinematic relationships between the six axes of the multi-axis machine.
However, while multi-axis machines represent a simplification of the conventional mechanical machines, all design calculation and gear theoretical considerations are still based on the theoretical basic machine model having a plurality of fixed machine settings. This practice has had the practical effect of limiting the available gear making processes of modern multi-axis gear making machines to replications of motions previously available only on older mechanical machines.
Methods have been proposed to modify gear forming and generating motions in order to more precisely control the tooth surface geometry of gears being produced. One such method is disclosed in U.S. Pat. No. 5,088,243 to Krenzer wherein additional motions are introduced which further control grinding processes with a flared-cup grinding wheel. Another method is disclosed in U.S. Pat. No. 5,116,173 to Goldrich in which variations in the location of the generating gear axis as well as variations in the orientation of the tooth surfaces of the generating gear are included in the generating process.
In either of the above methods however, the disclosed modifications would be implemented based on a plurality of fixed settings, of the type available on a conventional mechanical machine, to define the basic flank design. The fixed settings would be superimposed by movements defined directly in terms of the axes of the multi-axis machine without taking into account the axes of the theoretical basic machine. This combination of machine models yields an approximate tooth surface since superimposition of basic theoretical machine motions with actual motions from other machines provides a two-model surface which cannot be accurately represented either by tooth contact analysis or tooth flank surface data.
In any case, to date, gear calculations have been limited due to the fixed settings of the theoretical machine used to make those calculations, and it has never been realized to make gear theoretical considerations based upon all settings of the theoretical gear machine being free or active. Thus, although the multi-axis machine is capable of orienting the tool and work piece in almost any position relative to one another, the discovery of additional motions or freedoms has been constrained by the fixed settings of the theoretical basic machine.